Mauve Cherry Meadow
Manishness is apparently a dominate trait is LoTR. Well, Aside from elves where the child just got a choice to persue either heritage (Elrond was Half-Elven and immortal, his twin Elros chose the human path.)
If I remember there were hints that hobbits would eventually be absorbed into the general human population and culture after the end of the 3rd age. Most of the fantasy critters were on the decline and the elves leaving, this amusingly implies that orcs too were doomed to either dwindle (unlikely for goblins), or be absorbed as well (remember that fellow Bill Ferny at Bree?)
Then I really suppose this depends on how open they were to outsiders (in more ways than one, dur hurr hurr.) It's likely that many of the more reclusive and traditional hobbits simply dug themselves deeper and deeper into obscurity. Avoiding the prying eyes of the world at large.